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Answers
NOTE
A sum of money amounts to Rs 1056 in 4 years .
The SAME MONEY amounts to Rs 1248 in 7 years .
Note that this is the same original money.
Let us call that original money as P .
P is the Principal upon which interest will be applied .
P amounts to 1056 in 4 years .
P + I = A
Put the formula of I = P R T / 100
= > P + P R T / 100 = A
= > P ( 1 + R T / 100 ) = A
Given A = 1056 when T = 4
= > P ( 1 + R × 4 / 100 ) = 1056
= > P ( 1 + R / 25 ) = 1056
= > P ( 25 + R ) / 25 = 1056
= > P ( 25 + R ) = 1056 × 25
= > P ( 25 + R ) = 26400
= > P = 26400 / ( 25 + R ) ..................( 1 )
P amounts to 1248 in 7 years .
P + I = A
= > P + P R T / 100 = A
= > P ( 1 + R T / 100 ) = A
Given when T = 7 , A = 1248 .
= > P ( 1 + 7 × R / 100 ) = 1248
= > P ( 100 + 7 R ) / 100 = 1248
= > P ( 100 + 7 R ) = 124800
= > P = 124800 / ( 100 + 7 R ) .................( 2 )
From ( 1 ) & ( 2 ) :
26400 / ( 25 + R ) = 124800 / ( 100 + 7 R )
Cancel 100 both sides :
= > 264 / ( 25 + R ) = 1248 / ( 100 + 7 R )
Cross multiply both sides :
= > 264 ( 100 + 7 R ) = 1248 ( 25 + R )
= > 26400 + 1848 R = 31200 + 1248 R
= > 1848 R - 1248 R = 31200 - 26400
= > 600 R = 4800
= > R = 4800 / 600
= > R = 8
Hence Rate of interest is 8 %
Calculating the Principal from the rate
From ( 1 ) we have :
P = 26400 / ( 25 + R )
= > P = 26400 / ( 25 + 8 )
= > P = 26400 / 33
= > P = 800
The Principal was Rs 800
ANSWERS :
⇒ The rate of Interest was 8 % .
⇒ The sum of money was Rs 800 .
= (3x)³ - (y)³
= (3x-y) {(3x)² + 3xy + (y)²}
= (3x-y) (9x²+3xy+y²) [ANSWER]